기초과학VOD

BASIC SCI VOD

  •   >  
  • 연구동향
  •   >  
  • 기초과학VOD
Super Title 2018 KAIST Math. Colloquium
Title Oscillatory integrals over global domains
Speaker 김준일  (  Yonsei University  ) Date 2018-05-03
Host KAIST Place KAIST
VOD    
Given real valued polynomials $P$ on $\mathbb{R}^n$ and various unbounded domains $D \subset \mathbb{R}^n$, we consider the oscillatory integrals $$ I(P, D, \lambda) = \int_D e^{i\lambda P(t)} dt. $$ We establish a criterion on $(P, D)$ to determine the convergence of these integrals, and find the oscillation indices when they converge. These indices are described in terms of a generalized notion of Newton polyhedra associated with $(P, D)$. When $(P, D)$ for $D=\mathbb{R}^n$ satisfies the criterion of the vector polynomial version $(t_1, \cdots, t_n, P(t))$, we obtain the Strichartz estimates for the following general linear propagators: $ e^{it P(D)}(f)(x) \text{ where } D=\left(\frac{\partial_{x_1}}{i}, \cdots, \frac{\partial_{x_n}}{i} \right). $

이 페이지에서 제공하는 정보에 만족하십니까?